Related papers: Causal optimization method for imaginary-time Gree…
A method for deriving quantum kinetic equations with initial correlations is developed on the basis of the nonequilibrium Green's function formalism. The method is applicable to a wide range of correlated initial states described by…
In this paper, we present a quantum computational method to calculate the many-body Green's function matrix in a spin orbital basis. We apply our approach to finite-sized fermionic Hubbard models and related impurity models within Dynamical…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
The exact reduced density-matrix functional is derived from the Luttinger-Ward functional of the single-particle Green's function. Thereby, a formal link is provided between diagrammatic many-body approaches using Green's functions on the…
We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint…
Many-body Green's functions encode all the properties and excitations of interacting electrons. While these are challenging to be evaluated accurately on a classical computer, recent efforts have been directed towards finding quantum…
Computational difficulties aside, nonequilibrium Green's functions appear ideally suited for investigating the dynamics of central nuclear reactions. Many particles actively participate in those reactions. At the two energy extremes for the…
An end-to-end strategy for hybrid quantum-classical computations of Green's functions in many-body systems is presented and applied to the pairing model. The scheme makes explicit use of the spectral representation of the Green's function,…
Multi-electrode neurophysiological recordings produce massive quantities of data. Multivariate time series analysis provides the basic framework for analyzing the patterns of neural interactions in these data. It has long been recognized…
We present a quantum Monte-Carlo algorithm for computing the perturbative expansion in power of the coupling constant $U$ of the out-of-equilibrium Green's functions of interacting Hamiltonians of fermions. The algorithm extends the one…
Simulation methods are among the most ubiquitous methodological tools in statistical science. In particular, statisticians often is simulation to explore properties of statistical functionals in models for which developed statistical theory…
Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and…
Mendelian randomization (MR) is widely used to uncover causal relationships in the presence of unmeasured confounders. However, most existing MR methods presuppose linear causality, risking bias when the true relationships are nonlinear,…
Intensive longitudinal data, characterized by frequent measurements across numerous time points, are increasingly common due to advances in wearable devices and mobile health technologies. We consider evaluating causal mediation pathways…
Causal discovery is essential across various scientific fields to uncover causal structures within data. Traditional methods relying on observational data have limitations due to confounding variables. This paper presents an…
The single particle Green's function provides valuable information on the momentum and energy-resolved spectral properties for a strongly correlated system. In large-scale numerical calculations using quantum Monte Carlo (QMC), dynamical…
We propose an improved quantum algorithm to calculate the Green's function through real-time propagation, and use it to compute the retarded Green's function for the 2-, 3- and 4-site Hubbard models. This novel protocol significantly…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
Theoretical descriptions of non equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on truncation of the expansion of the many-body wave function, (ii) compressed representations of…
An important problem in many-body physics is to reconstruct the spectral density from the imaginary-time domain Green's function. Typically, the imaginary-time Green's function is generated by Monte Carlo methods. As the one-point fermionic…